corroboration

[R. Zander]

Bengt Oxelman wrote:

> Again,
>
> >> >witnesses), maximum parsimony (simplest hypothesis), and maximum posterior
> >> >probability (2/3)\(2/3 + 1/3) = .66. Of course we don't hang him.
>
> Would you hang him if the posterior probability was .95 or higher?

Well, maybe a good scolding...and only if the witnesses were unbiased, and other
due processes were observed. In the case of phylogenetic reconstruction, however,
our science hangs by exactly this thread.


> Although
> I hope you wouldn't hang him even if it was 1, I seriously doubt using a
> rejection level at all, if it can not be shown that the pieces of evidence
> (replicates) are drawn independently and with control of error (i.e. at
> random). When are cladistic characters drawn at random?

> Bootstrapping/Jackknifing can by increase the number of unreasonable trees
> (relative to strict parsimony), thus leaving fewer reasonable trees to
> choose from.

I disagree. Resampling works fine in other sciences when (1) there genuinely is a
much larger universe of characters, and (2) if the mathematical analysis uses
optimization, it is used for prediction and testing, not retrodiction. Phylogenies
cannot be tested directly, and an optimum must also be of high probability for a
reconstruction.


>
>
> >But in evolutionary studies, if a black ball supports one hypothesis and a
> >>white ball supports a second one, then we get, after much sampling (after
> >many >data sets are examined) a mixture of balls--a set of contradictions
> >that does >not change. Thus, optimal solutions that reappear with new data
> >sets do not >themselves increase the probability of the optimal solution.
>
> It is important here to define what the 'optimal solution' actually
> represents.

Optimum means best, by some criterion. I understand maximum parsimony, max
likelihood, maximum posterior probability, and minimum falsifiability, but exactly
what else the optimum solution is good for, if of low probability, is not obvious
to me.


> In the first case I assume you mean more_or_less, in the other
> the 'truth'. It could very well be the ratio of hypotheses, or simply the
> preferred hypothesis.  The balls could also represent the effect of a drug,
> black indicating positive response, white negative. Then you could perform
> a sign test, which certainly is dependent on sample size. You are right
> that the ratio of evidence is fixed, but our level of knowledge is usually
> so low that an initial qualitative measure is valuable.
>
> In another message, you wrote:
> >One must calculate posterior probability, which must be very high for a
> >>scientifically acceptable reconstruction.
>
> Does this mean that you reject all phylogenetic hypotheses which does not
> have high posterior probabilities (i.e. homoplasy levels below 5 % or
> something)?

As phylogenetic reconstructions, yes. Note, however, that many gene trees whose
probabilities add to a 95% credible interval may have subclades that are
identical, and these are decent reconstructions of a gene phylogeny.


> Hennig's reciprocal illumination could theoretically remove all
> homoplasy,

No. This seems logical, but if the procedure is not done with concern for
alternative reasonable "illuminations," probabilistically it is empty resolution:
like adding a 30X eyepiece to a microscope to get X3000 power. Optimizing parts of
an optimum to make it simpler is scientifically fruitless, though the results are
superficially impressive. I know, I've done it (functional ingroup/outgroup) and
it's so pleasing to get such a nicely resolved tree.

Don't get me wrong here. Parsimony analysis results in a pool of reasonable trees,
any one of which is worthwhile basing a classification on since any one of the
trees has considerable predictive power (geography, chemistry, etc.). Only if
there are no alternative reasonable trees does parsimony analysis reconstruct
anything about past relationships, however, and given the lack of a probabilistic
framework producing a confidence or credible interval, the size of the pool of
reasonable trees depends on the intuitive sense of a taxonomist familiar with the
group.

del here


Richard H. Zander
Curator of Botany, Buffalo Museum of Science
1020 Humboldt Pkwy, Buffalo, NY 14211 USA
bryo at paradox.net   voice: 716-896-5200 ext. 351